Theorems · Theorem · order theory
iSup_union
∀ {α : Type u_1} {β : Type u_2} [inst : CompleteLattice α] {f : β → α} {s t : Set β},
⨆ x ∈ s ∪ t, f x = (⨆ x ∈ s, f x) ⊔ ⨆ x ∈ t, f x- Defined in
- Mathlib.Order.CompleteLattice.Basic
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext, Quot.sound
- Assumes
- CompleteLattice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- iSupstatement and proof · cited by 2,415
- CompleteLatticestatement and proof · cited by 1,048
- iSup_congr_Propproof · cited by 247
- iSup_sup_eqproof · cited by 7
- iSup_orproof · cited by 3
Cited by8
Results whose statement or proof uses this declaration.
- iSup_splitproof · cited by 6
- Set.biUnion_unionproof · cited by 4
- sup_iSup_nat_succproof · cited by 3
- LieAlgebra.Basis.iSupIndep_rootSpaceproof · cited by 3
- Finset.iSup_unionproof · cited by 1
- iSupIndep.disjoint_biSup_biSup'proof · cited by 1
- LieAlgebra.Basis.root_mem_or_mem_negproof · cited by 0
- MeasureTheory.IsTightMeasureSet.unionproof · cited by 0